I presume the Roman Catholics still do it but does it have papal sanction? Do the main Protestant churches use it? And what about Judaism and Islam? Frankly it astonishes me that this medieval nonsense survives at all but with Hollywood constantly priming the pump I guess I shouldn’t be so surprised.
The Roman Catholics do, indeed, still have an official order of Exorcist, but it’s established under the individual bishops, not church-wide. And, for the record, it’s a lot harder to convince a priest that you’re actually possessed by demons than you might think. More likely, he’ll tell you to seek psychotherapy.
Anglicans also have official exorcism, with pretty much the same restrictions. Baptists, Methodists, Lutherans, Greek Orthodox another other mainline Christian churches do believe that demonic possession can be real, they just don’t have the level of ritual the Catholics and Anglicans do.
In fact, the 1949 exorcism that inspired the book and movie was actually put into motion by a Lutheran minister who then refered the child to a Catholic priest after psychiatric treatment was ineffective.
Hindus also believe in possession and exorcism – different concept, of course, but it’s still a thing.